Despite progress in human motion capture, existing multi-view methods often face challenges in estimating the 3D pose and shape of multiple closely interacting people. This difficulty arises from reliance on accurate 2D joint estimations, which are hard to obtain due to occlusions and body contact when people are in close interaction. To address this, we propose a novel method leveraging the personalized implicit neural avatar of each individual as a prior, which significantly improves the robustness and precision of this challenging pose estimation task. Concretely, the avatars are efficiently reconstructed via layered volume rendering from sparse multi-view videos. The reconstructed avatar prior allows for direct optimization of 3D poses based on color and silhouette rendering loss, bypassing the issues associated with noisy 2D detections. To handle interpenetration, we propose a collision loss on the overlapping shape region of avatars to add penetration constraints. Moreover, both 3D poses and avatars are optimized in an alternating manner. Our experimental results demonstrate state-of-the-art performance on several public datasets.